Optical super-resolution through super-oscillations

Most ideas for achieving super-resolution in optics are based on the recovery of evanescent fields which are commonly believed to be the necessary components to form subwavelength field concentrations. For instance, the famous Veslago-Pendry idea for a far-field super-lens is based on the recovery of evanescent information by "amplifying" the fading evanescent components in a slab of a negative-index material. However, evanescent fields may not be needed to achieve subwavelength concentration of light: according to a phenomenon called superoscillations, band-limited functions are able to oscillate arbitrarily faster than the highest Fourier components they contain. We also show that properly designed arrays of nano-holes can be used as a far-field imaging super-lens thus opening a new way of achieving optical resolution beyond Rayleigh limit, which is different from many existing approaches depending on the recovery of evanescent fields.